From the Etymological Dictionary

squeamish (adj.)
late 14c., variant (with -ish) of squoymous “disdainful, fastidious” (early 14c.), from Anglo-French escoymous, which is of unknown origin. Related: Squeamishly; squeamishness.
He was somdel squaymous
Of fartyng, and of speche daungerous
[Chaucer, “Miller’s Tale,” c. 1386]

What did disdainful mean in the later 14c? Squeamish today does not have a connotation of being disdainful. Here again from the Etymological Dictionary

disdainful (adj.)
“contemptuous, scornful, haughty,” 1540s, from disdain (n.) + -ful. Earlier was disdainous (late 14c.). Sometimes in early Modern English shortened to sdainful. Related: Disdainfully; disdainfulness.